Question

Can a number/unit of time be irrational? (Example: 3.14159... minutes)

Answer 1

Yes

Explanation:

Suppose it takes a snail `10` minutes to travel the length of one side of a square.

If it travelled at the same speed, how long would it take for it to travel the length of the diagonal of the same square?

Answer: `10sqrt(2)` minutes.

Or related to your example, suppose the snail takes `1` minute to travel the diameter of a certain circle. How long would it take for the snail to travel once round the circle at the same speed?

Answer: `pi` minutes.

Time is a continuous quantity. One reason we might think of it as discrete is since we use digital watches nowadays.